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High capacity, transparent and secure audio
steganography model based on fractal coding and chaotic
mapintemporaldomain
Ahmed Hussain Ali
1
&Loay Edwar George
2
&
A. A. Zaidan
3
&Mohd Rosmadi Mokhtar
1
Received: 7 July 2017 /Revised: 22 April 2018 /Accepted: 24 May 2018
#Springer Science+Business Media, LLC, part of Springer Nature 2018
Abstract Information hiding researchers have been exploring techniques to improve the
security of transmitting sensitive data through an unsecured channel. This paper proposes an
audio steganography model for secure audio transmission during communication based on
fractal coding and a chaotic least significant bit or also known as HASFC. This model
contributes to enhancing the hiding capacity and preserving the statistical transparency and
security. The HASFC model manages to embed secret audio into a cover audio with the same
size. In order to achieve this result, fractal coding is adopted which produces high compression
ratio with the acceptable reconstructed signal. The chaotic map is used to randomly select the
cover samples for embedding and its initial parameters are utilized as a secret key to enhancing
the security of the proposed model. Unlike the existing audio steganography schemes, The
HASFC model outperforms related studies by improving the hiding capacity up to 30% and
maintaining the transparency of stego audio with average values of SNR at 70.4, PRD at
0.0002 and SDG at 4.7. Moreover, the model also shows resistance against brute-force attack
and statistical analysis.
Multimed Tools Appl
https://doi.org/10.1007/s11042-018-6213-0
*Ahmed Hussain Ali
ahmedhussainali@siswa.ukm.edu.my
Loay Edwar George
loayedwar57@scbaghdad.edu.iq
A. A. Zaidan
aws.alaa@fskik.upsi.edu.my
Mohd Rosmadi Mokhtar
mrm@ukm.edu.my
1
Universiti Kebangsaan Malaysia, Bangi, Malaysia
2
University of Baghdad, Baghdad, Iraq
3
Universiti Pendidikan Sultan Idris, Tanjung Malim, Malaysia
Keywords Fractal coding .Least significant bit .Steganography.Information hiding .Logistic
map .Statistical steganalysis
1 Introduction
Information security is the practice of providing secure transmission of important data that
mainly consist of two main techniques, cryptography and information hiding [13]. Cryptog-
raphy renders the secret data to be meaningless and unreadable to the attackers. Information
hiding can be divided into two classes, namely, watermarking and steganography.
Watermarking achieves copyright protection or ownership by embedding watermarks inside
the media. Meanwhile, steganography hides and transmits confidential data and their existence
simultaneously [4,39]. The most common digital media used in data hiding are image, text,
audio, and video files. Audio steganography is an approach that hides secret information inside
an audio file. Due to the high sensitivity of human auditory system (HAS), hiding secret data
in the audio file is a challenge comparing with other media [15].
The performance of any data hiding technique depends on its hiding capacity, transparency,
and robustness [14,20]. Capacity or hiding capacity means the percentage of the size of the
secret file to that of the cover file and measures by handard percentage. On the other hand, it
can be represented by the number of the secret bits that can be embedded during a unit of time
and it is measured by bit per Second (bps), which sometimes called embedding rate or payload
[62]. Transparen cy means the closeness of property between the stego and reconstructed files
and the original cover and secret files, respectively. This parameter also means minimum
degradation and is inversely proportional to hiding capacity. Specifically, high distortion and
low transparency result in high hiding capacity [6]. Robustness indicates the resistance of stego
file to various attacks and its capability to retrieve secret message with a minimum error.
Robustness is the significant parameter in watermarking while transparency and hiding
capacity are the most important for steganography [8,41]. These parameters are contradictory
to each other. In particular, the increase in hiding capacity leads to degradation in the
robustness of secret message and transparency of stego file. The trade-off among these
parameters is complicated task [32,60].
Data hiding techniques, in general, can be classified into three main domains according to the
format of the cover file: temporal or time [25,29], transform [7,15,20,43,47]andcompressed [30,
36,55] domains. In the temporal domain, the cover data are modified directly to hide the secret data.
Thus, the techniques in this domain are considered simple and fast, but they are less robust to signal
processing. An example of such technique is LSB. In the transform domain, the cover samples are
transformed into a set of coefficients, while the secret data are concealed inside these coefficients to
enhance robustness and security. Examples of techniques in transfer domain are Discrete Wavelet
Transform (DWT), Fast Fourier Transform (FFT), and Discrete Cosine Transform (DCT).
On the other hand, some data hiding techniques adopt data compression techniques as a new
trend to decrease the bandwidth and the size of the secret data is compressed and then hidden into the
cover file. Data hiding techniques adopted data compression method can be classified under the
compressed domain. Vector quantization [30,56], fractal coding [17], and block truncation coding
[33,55] are the most common lossy or irreversible compression techniques for increasing hiding
capacity related to image steganography. However, such compression technique has not yet
implemented in audio steganography. Additional aspects on audio steganography are also discussed
by Djebbar et al. [14]andAlietal.[5] in greater details.
Multimed Tools Appl
In this study, an audio steganography model based on fractal coding and chaotic LSB is
proposed. This model exhibits high hiding capacity and preserves the transparency of the stego
audio. Given that it is a hybrid, it adopts two domains for data hiding, namely, time and compressed
domains. The HASFC model is also a blind method, which means that the embedded secret data can
be extracted from the stego audio without referring to the original cover audio [40].
The rest of the paper is organized as follows. Section 2shows the related work. Section 3
gives a summary of the methods adopted by the proposed model. Section 4presents the
proposed model and describes its phases. Section 5shows the experimental results and
discussion. Section 6is the summary points. Finally, Section 7and 8highlight the limitation
and conclusion.
2 Related work
In this section, the related works in audio steganography are discussed along with the
corresponding contributions in improving the hiding capacity through different approaches
and domains. In recent years, various audio steganography techniques have been proposed and
implemented. Nevertheless, it is only limited to temporal and transform domains. These
methods aim to minimize the tradeoff between the hiding capacity and transparency, which
are the significant parameters in each steganography technique [47].
2.1 Temporal domain
LSB is the widely used approach in the embedding process in the temporal domain [35,54].
LSB is also known as the replacement approach because the secret message is embedded by
replacing the rightmost bit of the cover samples. This approach presents advantages of
simplicity, ease of implementation, low distortion, and low computational cost. Owing to
these merits, LSB has been adopted in many steganography and watermarking techniques.
However, this approach is vulnerable to eavesdropping because of the imbalanced odd and
even samples caused by the embedding process.
LSB has been proposed recently in the following two studies. Kekre et al. [27] proposed
two approaches for embedding audio signal using different numbers of LSB depending on the
most significant bit (MSB) of the cover audio. They found that the number of LSBs used in
embedding can be up to seven, and that the number of LSBs depends on the MSB of the cover
samples. The authors used a 16-bit cover sample for their approaches. The results showed that
the obtained hiding capacity is between 35 and 70% of the cover file size. The signal to noise
ratio (SNR) of the stego file is 52 dB on average. Bazyar and Sudirman [10] on the other hand
proposed an embedding technique for increasing carrying capacity. They used an LSB
algorithm for embedding and shifting the embedding layer from the fourth LSB layer to the
seventh LSB layer. The results showed that the obtained hiding capacity is between 35 and
55%, and the SNR of the stego file is 62 dB on average.
2.2 Transform domain
DWT and DCT are used in the transform domain because of their capability to increase the
hiding capacity and robustness of steganography systems. Several other methods are proposed
in this particular domain.
Multimed Tools Appl
Sheikhan et al. [49] in 2010 suggested a method in the wavelet domain. In their method, the
secret signal is embedded in the selected coefficients using LSB based on the modified floating
three-level HAAR wavelet function. Floating number of bit is used in substitution, in which
the number of embedded bits depends on the sub-band energy for producing good SNR. The
findings showed an acceptable hiding capacity of 14.3% and high SNR and mean opinion
score (MOS) compared with those of other previous studies. Shahadi and Razali [45] proposed
a block matching algorithm based on discrete wavelet packet transform (DWPT). Matching,
scaling, and replacement are adopted in data hiding rather than LSB. Their proposed algorithm
obtains hiding capacity of 35%, more than 25 dB resistance to additive white gaussian noise
(AWGN), and recognizes secret message up to 25 dB [45]. Shahadi and Jidin [46] in the same
year also proposed an algorithm based on wavelet packet transform but with adaptive hiding
based on LSB. In this algorithm, the strength of cover samples and the matching of bit blocks
are the two factors that affect the hiding process. The results showed that the embedding
capacity can be up to 42% of the cover signal with minimum SNR of 50 dB.
Sheikhan et al. [50] proposed a method for hiding information in wavelet coefficients using
the LSB substitution technique. The cover signal is divided into several sub-bands using DWT.
The sub-band with a lower than or equal energy to the hearing threshold is used in the
embedding process. The SNR of the stego file is 76 dB, and the hiding capacity is 34% of the
cover file size on average. Shivdas [53] conducted sample segment comparison in the DCT
domain for hiding text or audio in an audio carrier. The hiding capacity is up to 25% of the
cover file size, and the SNR of the stego file is within 50 dB. Shahadi et al. [48] in 2014
proposed an audio steganography based on lifting wavelet transform (LWT) and adaptive
random embedding using weighted block matching. This scheme increases hiding capacity to
48% (up to 340 Kbps), SNR of above 35 dB, and lossless message retrieval. El-Khamy et al.
[15] proposed a scheme for concealing encrypted images using RSA in audio cover by sample
comparison in a DWT domain and coefficients selected using the pseudo number. The
experimental results show the embedding rate is 5698 bps which mean less than 1% hiding
capacity and 41.73 SNR stego fidelity. Moreover, the results demonstrate that the proposed
scheme is robust against some of the signal processing attacks as AWGN noise, MP3
compression and echo addition. El-Khamy et al. [16] proposed image in audio hiding scheme
for improving the hiding capacity, security and the robustness of the audio steganography
using two levels integer wavelet transform, wavelet coefficients modification, XOR, and
chaotic map techniques. Payload with 21,845 bps, a hiding capacity of 25% of the cover file
and SNR 44.6 dB stego fidelity are the obtained results from the proposed scheme.
3Mainmethods
This section briefly discusses the three main methods used in the HASFC model. Although
there are many techniques for embedding and compression, the proposed model adopts the
fractal coding, least significant bit and chaotic map for the reasons shown in next subsections.
3.1 Fractal coding
Data compression techniques in general can be classified into lossless and lossy compression.
Lossy techniques provide high compression ratio than lossless compression, however, the files
before the compression are not identical with the files after the compression while in lossless
Multimed Tools Appl
the files are indistinguishable [44]. In most cases, the deficiency of the quality of the
reconstructed audio, image or video files are not considered a critical issue while in other files
such as text, this it is a very important issue where small differences can led to different
meanings [28].
Fractal coding is a lossy compression technique that was introduced by Benoit Mandelbrot in
1975. Fractal geometry is the science concerning the property of fractal objects found in the real
world. The fractal concept is based on the existence of numerous similarities and redundancies in
most real-world objects [59]. Fractal coding was first used for image compression by Barnsley [9].
Jacquin [22] then extended Barnsley’s work using the mathematics of Iteration Function System
(IFS). In IFS, the output of the first iteration is considered the input to the second iteration and the
computational complexity is considered high. Jacquin finally established a practical Fractal coding
algorithm using Partition Iteration Function System (PIFS). In this technique, an image is divided
into two types of blocks, namely, overlapped domain and non-overlapped range blocks. Each range
block is then represented and encoded by set of IFS code. The IFS code consists of set of coefficients
that include the domain block index, scale and range mean.
Fractal coding is a prominent approach used for lossy data compression because of its high
compression ratio and accepted the quality of the reconstructed signal compared with those of
other techniques, such as DWT and DCT [21,38,51]. Unlike DCT and DWT, Fractal coding
also requires less computational complexity because its process does not require any transfor-
mation. Moreover, fractal coding presents an asymmetric property in which the encoding
process is time-consuming during the range–domain matching process while the decoding is
simple and fast [38,52].
Similar to other compression techniques, fractal coding consists of two main processes, namely,
encoding and decoding. The encoding process of fractal coding includes three steps [23,24]:
1. Partitioning input signal into non-overlapped (shifting the previous block by one block
size) range and overlapped (shifting the previous block by one pixel) domain blocks to
increase the domain blocks and the probability of finding a domain block that is more
similar to the particular range block.
2. Matching between range and domain blocks to produce optimum IFS coefficients for each
range block with minimum error using Eqs. (1)to(4):
x2¼σ2
rþssσ2
dþ2dr−2
n∑
n−1
n¼0
diri
ð1Þ
s¼
1
n∑n−1
i¼0diri−dr
σ2
d
;if σ2
d<0
0;if σ2
d¼0
8
>
>
<
>
>
:
ð2Þ
r¼1
n∑n−1
i¼0ri;¼d1
n∑n−1
i¼0dið3Þ
σ2
d¼1
n∑n−1
i¼0d2
i−d
2;σ2
r¼1
n∑n−1
i¼0r2
i−r
2ð4Þ
where x
2
is the error between the current range block and domain block;
Multimed Tools Appl
sis the scale parameter;
d, r is domain and range with nsamples respectively.
d
i
is the value of the i
th
sample in the domain block;
r
i
is the value of the i
th
sample in the range block;
d;rare the mean of the range and domain blocks, respectively;
σ2
d;σ2
rare the variances of the range and domain blocks, respectively.
3. Saving the optimum IFS coefficients for the decoding process
The decoding process is simple and straightforward. In this process, the affine mapping is
applied using the retrieved IFS coefficients and arbitrary samples by the following equation:
r0
i¼sd
i−d
þrð5Þ
where.
r0
iis the retrieved range block; sis the scale parameter;
d
i
is the value of the i
th
sample of the arbitrary block;
d;rare the mean of the stego and range blocks, respectively.
3.1.1 Fractal coding for data hiding
The proposed model adopts the fractal coding proposed in [2,3,11],whichisdesignedfor
image and audio compression after making amendments in order to use it in data hiding.
The amendments of the fractal coding algorithm are: (1) adopting two signals as input to the
fractal coding algorithm instead of one signal, (2) considering the cover audio as domain and secret
audio as the range to generate the cover and secret blocks and (3) the reconstructed secret signal is
obtained by applying the retrieved IFS codes on the stego data only once instead of using random
signal and repeat the process several times. To the best of our knowledge, fractal coding has not been
used in audio data hiding.
3.2 Least significant bit
Least significant bit (LSB) is one of the conventional substitution methods used in time domain data
hiding. The mechanism is to replace the LSBs of the cover samples with the secret bits directly.
Although it has several pros such as simplicity, low complexity, and high hiding capacity, it has
weak points such as low robustness against statistical analysis and it is vulnerable to attack [14,29].
The robustness of the LSB will be enhanced in the proposed model by integrating the chaotic map.
3.3 Chaotic map
The chaotic map is used due to the high sensitivity of the initial parameters and to scatter the
secret data in a way that could not be exploited by an attacker for detection [25]. The logistic
map is the simplest chaotic map that is adopted in the proposed model to randomly select the
cover samples for embedding the secret bits and can be represented by:
xnþ1¼tx
n1−xn
ðÞ ð6Þ
where 0 ≤t≤4, x
0
ϵ(0, 1).
Multimed Tools Appl
The characteristic of the logistic equation depends on the parameters tand x
0
[19,
61]. The logistic map is adopted to chaotically select the samples of the cover audio
Embedding Phase
Extraction Phase
Pre-Processing Fractal
Encoding
Generating Stego
audio
IFS Extraction Fractal decoding and
reconstruction
Embedding
Fig. 1 Proposed model
Embedding
Generate
Ste
g
o File
Ste
g
o audio
Combine the modified
cover audio
Merge data with the
header information
No
Decimal to binary
converter
LSB
Cover
sam
p
les
IFS codes for all
secret blocks
Selected Cover
sam
p
les chaoticall
y
Select bits from
binary sequence
chaotically
Pre-processing
Load and
split audio
Data from
the header
Generate fixed
non-overlapped
secret and
overlapped cover
b
locks
Secret Audio
Cover Audio
Secret
block
Compute mean
and variance
for secret and
cover
Generate matrix
of pseudo
random
numbers
Sort in
ascending
order
Matrix of
chaotic
indexes
Select cover
block from
cover pool
Match secret with
cover
b
lock
Compute IFS
code and update
the error
No
Yes
More
cover
b
locks?
Register the IFS code
for current secret
block that has
minimum error
Fractal Encoding
More
secret
b
locks?
Yes
Skey1
Skey2
Fig. 2 Sub-model (data embedding Phase)
Multimed Tools Appl
for embedding rather than the sequential manner. The two parameters are considered
the secret keys in embedding and extraction.
4Proposedmodel
This section discusses the details of the proposed model. The main objective of
HASFC model is to improve the hiding capacity and maintain the transparency of
the cover audio compared with those of other methods. The HASFC model employs
fractal coding for encoding and compressing the secret audio, which accordingly
increases the hiding capacity of the cover audio size. Moreover, adopting fractal
coding offers security as fractal coding encodes the secret samples into a set of IFS
codes. These IFS codes are then hidden into cover samples instead of the original
secret samples. Moreover, any third party who finds the IFS codes will not understand
the secret message without the specific method. Logistic map with LSB is adopted as
an embedding technique to enhance the security of LSB method.
In this model, the initial parameters of the chaotic map are used as a secret key
required in the sender and the receiver sides. Similar to other steganography tech-
niques, HASFC model consists of two main phases, namely, embedding and extrac-
tion as shown in Fig. 1. The embedding phase is composed of four processes which
are pre-processing, fractal encoding, embedding and generating stego audio, whereas
extraction phase consists of two processes, IFS extraction and fractal decoding and
reconstruction.
4.1 The data embedding phase
The data embedding phase is executed by the sender as shown in Fig. 2.Inthis
phase, we denote the cover audio as C={c(i), 1≤i≤L1}whereL1 represents the
number of samples that are used for embedding. Accordingly, the secret audio is
represented as S={s(i), 1≤i≤L2}whereL2 signifies the number of secret samples to
hide. The Cand Sare then partitioned into blocks with a number of samples known
as BL. Next, the cover audio Cis partitioned into a number of blocks L1
BL,whereblc
iðÞ 1≤i≤L1
BL
refers to the i
th
block of Cfile whereas, the secret audio Sis
partitioned into L2
BL blocks where bls(j){1≤j≤L2/BL}isthei
th
block of S.This
phase also involves the computation of the mean and the variance of both the cover C
and secret Srespectively. The mean and variance of the i
th
cover block are repre-
sented as Mc¼mc iðÞ;1≤i≤L1
BL
and Vc¼vc iðÞ;1≤i≤L1
BL
. Similarly, the secret mean
and variance for the i
th
secret block are represented as Ms¼ms iðÞ;1≤j≤L2
BL
and
Vs¼vs jðÞ1≤j≤L2
BL
. The secret blocks are represented by a set of IFS codes,IFS =
{ifs(i), 1≤i≤L2}wheretheifs(i)isthei
th
IFS code for the i
th
secret block bls.The
next step in the embedding process is the random selection of the cover samples for
hiding the IFS. The chaotic vector CH = {ch(i), 1≤i≤L} is used for this purpose with
Lindexes where L=L1. The three factors that are used in the matching process are
the scale factor Scl, the approximate error x
2
and the predefined error threshold Th.
Multimed Tools Appl
4.1.1 Pre-processing
Pre-processing under the embedding phase consists of the following two main tasks.
Construct blocks and compute mean and variance This subprocess is responsible for
constructing the cover and secret blocks. Moreover, the mean and variance for all cover and secret
blocks are also computed in this subprocess. Algorithm 1 illustrates the pre-processing process:
Generate chaotic indexes process Chaotic indexes are generated using Eq. 6, and these
indexes will be used in selecting the cover samples instead of the sequential manner in the
traditional LSB. In this proposed model, two secret keys which are the initial parameters of the
chaotic map are considered as a secret key provided in sender and receiver sides. The
algorithm is as follow:
Multimed Tools Appl
4.1.2 Fractal encoding process
In the process, the secret and cover blocks are considered as the range and domain pools,
respectively. The IFS coefficients consist of the index, scale, symmetry, and the mean of the
secret blocks. The total number of bits of the IFS for all secret blocks is less compared with the
number of bits required to hide the actual secret samples. The binary sequences of IFS are used
in the embedding sub process. The details of this process are illustrated in Algorithm 3:
An example of the fractal encoding process For example, when the secret and cover
audio have the same size of 44,100 samples and each sample has 16 bits. Hence, the secret size
will be 705,600 bits (44,100 × 16) and the cover audio are insufficient to embed secret data of
less than 44,100 bits (given that 1 LSB for each cover sample from 16 bits is used for
embedding). Fractal coding is utilized to encode the secret block to the minimum number of
bits. In this case, the block size of 32 samples is selected based on Eq. (7).
In the encoding process, instead of embedding each secret block with actual samples that
require 512 bits for each block (32 × 16), each block will be encoded using fractal coding by
only 31 bits. The IFS code is 16 bits for index +6 bits for quantized scale +1bit for symmetry
+8 bits for the mean of the secret block. In this case, the compression factor of each block is
16.8 (512/31). Given that the number of secret blocks is 1378 samples (44,100/32), the total
number of bits required to represent the secret data is reduced from 705,600 bits to 42,765 bits
(1378 × 31 + 47 header information), with a compression ratio of around 93.9%.
Multimed Tools Appl
4.1.3 Embedding process
When the encoding process finished, IFS coefficients are embedded in the cover audio samples
after converting them into a sequence of binary bits using 1 LSB of 16 bits per sample.
Algorithm 4 explains the embedding process.
4.1.4 Generate stego audio process
Generation of the stego audio is the final step in the data embedding phase. The algorithm as
follow:
4.2 The data extraction phase
On the recipient side, the data extraction phase is taken place which is fast and simple, and it is
divided into two processes: extraction and fractal decoding-reconstructing audio secret audio.
The process begins with extracting the LSB from the stego samples then regenerating the IFS
codes, followed by applying fractal decoding to reconstruct and create the reconstructed secret
audiofileasinFig.3. The stego audio st = {st(i); 1≤i≤L} is the input file to this process with
Lnumber of samples. The reconstructed secret block, rbls(i){1≤i≤L4)withL4blocks, rbls(i)
is the i
th
reconstructed secret block. The output from this process is the reconstructed secret
samples rec = {rec(i); 1≤i≤L3}withL3 number of samples. The number of samples of rec
should equal to the number of samples of S, so that L3=L2.
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4.2.1 Extraction process
The LSB bits of the stego audio samples are collected in the same chaotic way as in the
embedding process by using the secret key that retrieves the IFS coefficients. The retrieved
coefficients are then used to reconstruct the secret blocks that are later used in the decoding
process to reconstruct the secret audio. Algorithm 6 illustrates the extraction process.
4.2.2 Fractal decoding and reconstruction process
The fractal decoding process is performed in this process. The process is considered fast and
simple because of applying the affine mapping using Eq. (5) on the stego blocks and the IFS
Fractal Decoding and
Reconstruction
Reconstructed
Secret file
Build header
file
Create
reconstructed
secret data
Fractal decoding
Build
reconstructed
secret blocks
Combine
reconstructed
secret blocks
Extraction
Stego
Fil
e
Load stego
file data
Select Stego
samples
chaotically
Retrieve
the IFS
codes
Generate chaotic indexes
using secret keys
Skey1
Skey2
LSB
gathering
Reorder the
binary
se
q
uence
Fig. 3 Sub-model (data extraction phase)
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codes for retrieving the array of the secret samples. After obtaining the array of the recon-
structed secret samples, the header for the retrieved secret audio is created. Finally, the
reconstructed secret audio is generated as shown in algorithm 7.Example of the fractal
decoding process The decoding process is straightforward, and it is performed using the IFS
code of each secret block and the particular stego block using the index parameter of the IFS
code parameter. Using Fractal decoding, the approximation of each secret block can be
constructed. For instance, suppose the block size is 8 samples and the secret block that want
to be encoded with these values (133,134,135,136,138,140,142,143). During the encoding
phase, suppose the best matching cover block to this particular secret block using cover-secret
mapping algorithm is (133,134,132,3131,130,129,128,126) and the IFS code of this secret
block is (0, 138, 0, −14). In decoding phase, using fractal decoding and the particular stego
block using the IFS code, the reconstructed secret samples can be obtained such as this
(134,133,136,137,139,140,141,144).
5 Experimental results and discussions
The hiding capacity, transparency of the stego audio and the security of the HASFC model are
presented through series of experiments in this section. The experiments use objective and
subjective metrics presented in section 5.1 for evaluating the performance of the HASFC
model in relation to the transparency of the stego audio, the hiding capacity, the statistical
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steganalysis tests in terms of histogram distribution and the fourth first moments and the
security of the HASFC model. Moreover, comparison to related schemes is also conducted.
The results from these experiments are used to assess the performance of the model with
regard to the above-mentioned properties. Finally, the results of HASFC model are compared
with the results reported in related schemes. HASFC model is developed using Java Eclipse
EE IDE for Web Developers Luna SR2 Package 4.4.2 on the Intel® Core™i5–4590 CPU @
3.30 GHz 4GB RAM with Windows 7 Professional 64-bit operating system.
In order to evaluate the performance of the proposed model and to compare the perfor-
mance with the related work discussed in section 2, the same audio specifications have been
adopted. For this reason, uncompressed audio files are used as secret and cover audios, which
were selected from the GTZAN dataset [57,58]. The specifications of the audio files used in
the experiments are listed below in Table 1.
5.1 Measurement metrics
In order to evaluate the performance of the proposed model, two different tests are adopted in
the form of objective and subjective test. In the objective test, Mean Square Error (MSE), Peak
Signal-to-Noise Ratio (PSNR), Signal-to-Noise Ratio (SNR) and Percentage Root Mean
Square Difference (PRD) and Hiding Capacity (HC) are used. On the other hand, Subjective
Difference Grade, namely (SDG) is used for the subjectivity listening test.
These metrics are used to support the theory behind the transparency and the hiding
capacity as follow:
5.1.1 Transparency
The following metrics are used to gauge the performance of the proposed model in terms of
transparency:
&MSE is the average square of the differences between the input and output signals and can
be defined as [36]
MSE ¼1
N∑
N
i¼1
s1i
ðÞ
−s2i
ðÞðÞ
2ð8Þ
where s1(i) and s2(i) are the i
th
samples of the input and output signals, and Nis the number of
signal samples. When this value decreases to zero, the fidelity of the input and output signals
becomes similar.
Tabl e 1 Audio files specification Specification
Bit per sample 16
Sample rate 44,100
Channel Mono
Audio type Speech
Music
Duration in Seconds 1–10
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&PSNR measures the maximum signal to noise ratio of a given signal. PSNR is given by [36]
PSNR ¼10 log10
2n−1ðÞ
2
MSE
! ð9Þ
where nis the maximum number of bits used to represent each signal sample.
&SNR measures the distortion in the fidelity between two signals, input, and output. SNR is
expressed as [26]
SNR ¼10 log10
∑
N
i¼1
s1iðÞ
2
∑
N
i¼1
s1iðÞ−s2iðÞðÞ
2
ð10Þ
where s1(i) and s2(i) are the i
th
samples of the input and output signals, and N is the number of
signal samples. The SNR should is more than 20 dB to be acceptable as declared by the
International Federation of the Phonographic Industry (IFPI) [12,31].
&PRD measures the percentage of root mean square differences between two signals The
PRD [42] is calculated based on the following equation
PRD ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
∑
i
Xi−Yi
ðÞ
2
∑
i
X2
i
v
u
u
u
tð11Þ
where X
i
is the first signal and Y
i
is the second signal. PRD values are ranged from 0 to 1, being
0 as the ideal value.
&SDG metric is used to evaluate the perceptual quality of the stego signal subjectively
which is implemented by human listeners. The score of the SDG is ranged from 1 to 5,
with higher values indicate better quality of the audio signal. SDG is similar to PEAQ
except the latter is implemented by software simulating the human auditory system [1,26].
5.1.2 Hiding capacity
The following metric is used to explain the hiding capacity of the proposed model.
-HC is the essential factor for evaluating any steganography technique and can be
calculated by [37]
HC ¼Secret file size
Cover file size 100Þ
ð12Þ
5.2 Transparency tests
Transparency refers to the perceptual similarity between the fidelity of cover and stego audio.
Two experiments are conducted to explore the transparency of the HASFC model using
different audio file types and block sizes.
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5.2.1 Various audio file types
This objective of this experiment is to evaluate the transparency using two tests, objective and
subjective with various speech and music files as cover and secret audios. MSR, SNR and
PSNR, PRD and SDG are used to justify the transparency accomplished by the HASFC
model. The experiment highlights the applicability of HASFC using various types of Audio
files. Different files are used as cover and secret audio with 220,500 and 44,100 samples,
respectively. The block size in this experiment comprises of 7 samples based on Eq. (7). This
specific selection of secret audio size, cover audio size, and block size is due to that the secret
audio with this size cannot be hidden inside the cover audio with a block size of fewer than 7
samples. If the size of the secret audio must be increased, then the block size must also be
increased.
The results of the objective test are shown in Table 2and Fig. 4. It shows that HASFC
model can be used to hide any type of audio files into another file and produced stego audios,
such as speech in music or music in speech, with high fidelity, regardless of the type of file
since the average of the SNR is above 20 dB [12,31]. The average SNRs for all types of audio
file are approximately 70.5 and 41.7 dB for the stego and reconstructed secret audios,
respectively. The PSNR is 99.5 dB on average for the stego audios and 47.4 dB for the
reconstructed audios while the average PRD value is 0.0002.
The transparency of the stego file generated by HASFC model is preserved since the
distortion of the cover file is reduced by using fractal coding that compresses the secret
samples before embedding.
Subjective listening test is also used to evaluate the perceptual quality of 8 stego audio
signals generated by the HASFC model with the hiding capacity of 100% based on the SDG
value. In this test, the cover and the stego audio signals are presented to 7 experts working in
acoustics research group and steganography field. They listen to each audio file for several
times and asked to evaluate the similarity between the audio signals by using a standard
measurement. The scores that were given are shown in Table 3.
Table 3shows the average SDG value of 4.7 that is derived from the 8 stego audio signals
with each signal performing above the minimum acceptable value of 4. These results show that
the stego signals generated by the proposed model and the cover signals yield similar
subjective quality.
Table 2 The fidelity of stego and reconstructed files using several secret and cover audio types
Cover Secret Stego Reconstructed
MSE PSNR SNR PRD MSE PSNR SNR
Dialogue Female 0.46 99.6 73.6 0.0002 1.28 47 41.1
Jazz 0.46 99.6 73.6 0.0002 1.40 46.6 40.7
Vlobos 0.46 99.6 73.6 0.0002 2.15 44.7 38.9
Female Dialogue 0.46 99.6 69.1 0.0003 2.42 44.2 38.4
Jazz 0.46 99.6 69.1 0.0003 0.57 50.5 44.6
Vlobos 0.46 99.6 69.1 0.0003 0.55 50.6 44.8
Jazz Dialogue 0.47 99.5 69 0.0003 2.43 44.2 38.4
Female 0.47 99.5 69 0.0003 0.71 49.6 43.7
Vlobos 0.47 99.5 69 0.0003 0.72 49.5 43.6
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The results of the objective and subjective tests show the high transparency of the HASFC
model from adopting the fractal coding and LSB method in the embedding process. For this
reason, there is no significant audible distortion resulted from the embedding process that able
raise suspicion on the existence of secret messages in the generated stego signal. Such
substantial results are directly influenced by the block size in the encoding process of the
fractal coding. Further analysis on the effect of block size to the transparency is presented in
the next subsection.
5.2.2 Different block sizes
This specific experiment aims to determine the effect of block size on the fidelity of stego and
reconstructed audios. The secret audio used in this test is the vlobos, while the cover audio
used are jazz,female, and voice. The audio size is fixed for the secret and cover audio of
220,500 and 44,100 samples, respectively.
The results in Fig. 5reflect the effects of block size on the fidelity of stego and recon-
structed secret audios. The SNR of the stego audio is directly proportional to block size,
whereas that of the reconstructed secret audio is inversely proportional to block size as shown
in Fig. 6that exhibits the differences between the original cover and the stego and those
between the secret audio and reconstructed secret audios of different block sizes for the above
two cases.
The block size is an important step for obtaining an acceptable SNR value, which is related
to the encoding process. During the encoding process, when the block size is increased, the
0
20
40
60
80
Female Jazz vlobos Dialogue Jazz vlobos Dialogue Female vlobos
Dialogue Dialogue Dialogue Female Female Female Jazz Jazz Jazz
SNR
Secret and Cover Files
Stego
Reconstrucon
Fig. 4 Fidelity of stego and reconstructed files using several secret and cover audio types
Tabl e 3 The average SDG values Audio No. Audio Name SDG
1Dialogue4.6
2Female 4.8
3Jazz 5
4 Voice 4.6
5 Undergrad 4.4
6Dialogue4.6
7 Undergrad 5
8Jazz 4.8
average 4.7
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number of IFS is decreased. As a result, the number of secret bits for embedding is decreased
due to less distortion to the audio cover file and hence a higher transparency is achieved.
66
68
70
72
74
76
78
80
1015202535
SNR
Block Size
Vlobos-
Jazz
Female-
Voice
34
35
36
37
38
39
40
41
1015202535
SNR
Block Size
Vlobos-
Jazz
Female
_Voice
Fig. 5 Effect of block size on the fidelity of (left) the stego, (right) reconstructed file
(1)
(2)
(3)
(4)
(5)
(6)
(a)
(1)
(2)
(3)
(4)
(5)
(6)
(b)
Fig. 6 Effect of block size using music files, Vlobos, Jazz as a secret and cover audio respectively. aOriginal
cover and stego audio. bOriginal secret and reconstructed files, using different block sizes of 10, 15, 20, 25 and
35
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Figure 6shows the result of hiding the audio signal Vlobos in Jazz. In Fig. 6a, the signal (1)
represents the original cover audio while the signals from (2) to (6) are the stego audios after
the hiding process. It is clear that the cover and stego audio show close similarity under block
sizes of 10, 15, 20, 25, and 35. Figure 6b represents the signal of the original secret (1) and
reconstructed secret audios (2) to (6) using different block sizes. Some changes appear on the
reconstruction signals (2) to (6) when block size increases compared with the original secret
audio represented by signal (1).
5.3 Hiding capacity test
The objective of this experiment is to show the hiding capacity that can be achieved using the
HASFC model. HC metric, Eq. (12) is used to explain the achieved hiding capacity theoret-
ically. This experiment also demonstrates the effect of block size on hiding capacity. Here, the
cover audio voice,vlobos, and female with 220,500 samples are used. Meanwhile, the secret
audio consists of jazz, voice, and female with different file sizes. Speech into music, music into
speech, and speech into itself are used in this experiment to investigate the effect of block size
on hiding capacity. As shown in Table 4, different block sizes are used and the selection is
conducted using Eq. (7) and the hiding capacity is measured using Eq. (12).
The results in Table 4show that, when hiding capacity is increased, block size must also be
increased and thereby decreasing the fidelity of the stego and reconstructed audios. Based on
the results, HASFC model has shown to hide secret audios with 100% hiding capacity of the
cover audio size with SNR of 37.4 dB on average for the reconstructed audio. The proposed
model also maintains the fidelity of the stego audio at approximately 70.4 dB. These results
further justify the adaptation of the fractal coding technique in the HASFC mode.
The integration of the fractal coding in the HASFC model has significantly improve the
hiding capacity up to 100% of the cover size. This is directly related to the fractal coding that
able to compress the secret samples with high compression ratio. Therefore, the block size is
the effective factor in the encoding process as shown in the previous paragraph.
Table 4 Effect of block size on hiding capacity with different secret audio sizes using optimum block size
samples
Cover
Secret
Cover
Samples
Secret
Sample
Block size
samples
Hiding
capacity%
Stego
SNR
Reconstructed
SNR
Vo i c e
Jazz
220,500 44,100 7 20 71.1 42.6
88,200 14 40 71.1 41.2
176,400 27 80 71 38
220,500 34 100 71 37.2
Vlobos
Female
220,500 44,100 7 20 71 42.2
88,200 14 40 71 39.2
176,400 27 80 70.8 38.5
220,500 34 100 70.8 38.1
Vo i c e
Vo i c e
220,500 44,100 7 20 71.1 41
88,200 14 40 71.1 39.3
176,400 27 80 70.9 37.3
220,500 34 100 70.9 37.2
Female
Jazz
220,500 44,100 7 20 69.1 44.6
88,200 14 40 69.1 41.1
176,400 27 80 69 38
220,500 34 100 69 37.3
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5.4 Steganalysis tests
The objective of the steganalysis is to find any marks about the presence of the secret audio
into the cover audio. HASFC model is a type of blind steganography in which the extraction
process does not need the original cover audio to reconstruct the secret signal. In the case of the
blind steganography which had no database that can be used to extract the secret data,
steganalysis depends on the statistical analysis of the signal variation to classify the signal
as a stego or cover audio. There are several steganalysis methods [7,8,18,47] proposed for
audio signals. In this section, the resistance of the HASFC model against two statistical
steganalysis, histogram [7,47]andfirst fourth moments statistical steganalysis [8,47]is
discussed since these two steganalysis methods are typically used for blind steganography
technique that is similar to the HASFC model.
5.4.1 Histogram attack
In relation to the histogram attack, we conduct two experiments using different cover and
secret audio. Histogram Error Rate (HER) [43,47]usingEq.(13) is adopted to find the
histogram error between the original cover and the stego audio produced by the proposed
model. Figure 7presents the HER value and the histogram of the original cover audio before
and after embedding the secret audio using hiding capacity 100% of the cover audio with a
block size of 50 samples.
HER ¼
∑
N
i¼1
His cðÞ−His sðÞðÞ
2
∑
N
i¼1
His cðÞ
2
ð13Þ
where His(c) and His(s) is the histogram of cover and secret audio.
(a)
Left: Original cover
Right: stego
HER= 0.0431
(b)
Left: Original cove
r
Right: stego
HER= 0.1278
Fig. 7 Histogram error avoice-rock and bjazz-female
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Based on the results in Fig. 7, the differences between the cover and its stego audio are less
than 0.2 and the variation is not observed, so the proposed model is undetectable through
histogram attack.
5.4.2 Fourth first moments
The HSAFC model is also evaluated using fourth first moments [8,47] which is statistics
measurements that exhibit the differences between the cover and secret signal. The moments
produce the function of the distribution of two signals. These moments are average (μ),
variance (σ), skewness (s), and kurtosis (k) as in Eq. (14)to(17), respectively. This test
calculates the difference ratio DR using Eq. (18) which represents any of these four moments
for cover and stego signal. When the values of DR are below 10%, this indicates that the stego
signal can resist the statistical steganalysis [8].
μ¼
∑
n
i¼1
si
nð14Þ
σ2¼
∑
n
i¼1
si−μ
ðÞ
2
n−1ðÞ ð15Þ
sk ¼
∑
n
i¼1
si−μðÞ
3
n−1ðÞσ3ð16Þ
k¼
∑
n
i¼1
si−μðÞ
4
n−1ðÞσ4ð17Þ
D¼100 Mc−Ms
Mc
ð18Þ
Where s
i
is the input signal and nis the size of S,Mc,Ms are any fourth first moments of
cover and secret audio, respectively.
The results listed in Table 5show the differences ratio using various cover audios. The DR
of the four moments for this test is less than 0.08 in all cases. This implies that it is not easy for
steganalysis to identify the stego signal based on the statistical analysis.
Table 5 Statistical analysis tests for HASFC: DR using fourth first moments
Cover Secret HER Mean Variance Skewness Kurtosis Stego SNR Reconstructed SNR
Voice Rock 0.0431 0.0810 0.0002 0.0002 0.00005 72.6 35.1
Jazz Female 0.1278 0.0789 0.0014 0.0035 0.0057 70.5 36.8
The average 0.0799 0.0008 0.0018 0.0028 71.55 35.95
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In order to compare the proposed model with other related methods in terms of hiding
capacity and statistical steganalysis, Table 6presents the comparison of the proposed model
and two methods entitled as HT_EWM [8] and LAS_LWD [47]. These two methods are
selected since their proposed schemes are evaluated by statistical steganalysis in the time
domain. It can be noticed that the HSAFC produces an acceptable DR values even with
achieving 100% hiding capacity with a slight increase in the Mean moments. The comparison
of HASFC with HT_EWM and LAS_LWD gives evidence that HASFC outperforms the two
methods and has an acceptable result regarding the statistical analysis and the hiding capacity.
5.5 Security test
Robustness against attacks is considered an important issue in data hiding. In fact, the security
of the information system depends on the secret key rather than the privacy of the scheme [31],
so in order to enhance the security of HASFAC, two secret keys are adopted using logistic map
function to generate two chaotic sequences used for selecting the secret bits to be hidden and
the cover sample for embedding as well. Each key consists of two values which are the initial
parameters of the used chaotic map, rand x
0
, these values are within the range of (0,4) and
(0,1) respectively, so these values are represented by double values with 64 bits. Hence the
number of possible random numbers using the two keys is 2 to the power 256 (2
64
×2
64
×
2
64
×2
64
) which is (1.1579209 × 10
77
). The attacker systematically checks all possible num-
bers until the correct one is found.
Let’s assume the attacker has the fastest supercomputer in the world which is Sunway
TaihulLight with about 10,649 processing unit and ability to calculate 93,014 trillion processes
per second (https://www.top500.org/lists/2017/06/). Also, we assume that each number test
equal to one process. In fact, the attacker can do many processes to test each number at any
particular time. Now, we can calculate the time that attacker needs to do brute force attack:
Number of possible random numbers ¼1:1579209 1077
Computer can d o ¼93;014 trillion process=second
Time ¼number of possible numbers=processesper second
Time ¼1:2448888 seconds;which is equal to3:9475 1052 years approximately:
Table 6 Statistical analysis DR comparison for HSAFC and some related methods
Methods HASFC LAS_LWD [47] HT_EWM [8]
Hiding capacity % 100 25 33
Four First moments Mean 0.0799 0.2304 <1.2
Variance 0.0008 0 <0.7
Skewness 0.0018 0.0004 <0.2
Kurtosis 0.0028 0.0005 <0.8
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This is an ample time duration that is required to break the random numbers of the HASFC
model. Furthermore, HASFC model is more sensitive to the modification of the secret keys. To
illustrate this effect, two experiments are conducted: one is to present the effect of slightly
modifying of the x
0
and the second is the altering of the t value, and we attempt to extract the
secret audio from a stego-audio. Jazz and voice are used in these experiments as a cover and
secret audio, respectively.
The results in Fig. 8(3) and 8(4) show that the reconstructed audio signals are significantly
different from the original signal in Fig. 8(1) even with small changes in the initial parameters.
For this reason, the security of the HASFC model have been enhanced by adopting the chaotic
map method. This is due to the ability of the chaotic map to generate greater randomness
through highly sensitive initial values.
5.6 Comparison to related schemes
For the final experiment, the performance of the proposed model is compared with that of the
schemes proposed in related work that contribute to enhancing hiding capacity and transpar-
ency in audio steganography. These schemes can be divided into time and transform based
methods. Multi LSB embedding technique is based on the temporal domain, while DWT and
DCT are based on the transform domain. The audio file specifications for these different
schemes are listed in Table 6.
For the HASFC, the selection process comprises of three speech files namely dialogue,
female, and voice along with three music files namely jazz, unpoco, and vlobos that come with
different sizes ranging from 1 to 11 s. The comparison is conducted in terms of hiding capacity
and fidelity based the published results that are available from these different schemes. In the
comparison, Eq. (12) is used to compute hiding capacity and Eq. (10) for fidelity across all the
schemes. Table 5is sorted according to the publication year of the related articles.
Table 7presents the results of comparison between HASFC and some selected related
schemes. Since the proposed model adopts temporal domain using LSB, a comparison with
other LSB schemes, specifically with Kekre et al. [27] and Bazyar and Rubita [10]were
conducted. Based the results, the highest hiding capacity was obtained by Kekre, with 70%
hiding capacity of the cover audio that uses multiple LSB up to 7 LSBs. On the other hand, the
proposed model only exploits 1 LSB for embedding the encoded secret samples and with
(1)
(2)
(3)
(4)
Fig. 8 (1): original secret audio. (2): secret audio extracted with NC = 0.9999. (3): secret audio extracted after
replacing t=0.59byx
0=
0.58 with NC = 0.0.6991. (4): secret audio extracted after replacing x
0
= 3.6 by x
0=
3.61
with NC = 0.6985
Multimed Tools Appl
hiding capacity of 100% of the cover audio size. Therefore, the HASFC model outperforms the
scheme proposed by Kekre by increasing 30% of the hiding capacity. At the same time, the
HASFC model has also improved the fidelity outcome of the stego audio between 8%–18%
when compared to the SNR values by Kekre and Bazyar respectively.
Subsequently, in order to highlight the overall potential of the HASFC, a comparison with
other schemes that adopt transform domain was therefore conducted on Sheikhan [49],
Shahadi [45], Shahadi [46], Sheikhan [50], Shivdas [53], Shahadi [48], El-Khamy [15]and
El-Khamy [16]. Comparable to the temporal domain, the hiding capacity of the cover audio
and the transparency of the stego audios, were analyzed for comparison between the different
schemes. For the hiding capacity, the highest hiding capacity in this particular domain is 48%
by Shahadi [48]. The HASFC performs better in this scheme by increasing the hiding capacity
by 52 to 100% of the cover audio size. The principle behind the increasing the hiding capacity
is illustrated in section 4.1.2. Additionally, the HASFC has successfully preserved the stego
audio fidelity at 70 dB, well above the acceptable 30 dB level but marginally lower than the
76 dB result previously attained by Sheikhan [50].
Figure 9virtualizes the result in Table 7 in a two-dimensional chart that represents the
relation between hiding capacity and fidelity between HASFC and the related schemes, which
distinctly shows HASFC surpasses the others in these two areas.
Table 7 Comparison of HASFC and related schemes
Schemes Hiding capacity (%) Stego SNR Reconstructed SNR
Sheikhan [49] 2010 14.3 49 –
Kekre [27] 2010 35–70 52 –
Shahadi [45] 2011 35 25 –
Shahadi [46] 2011 42 50 –
Sheikhan [50]2011 34 76 –
Shivdas [53] 2014 25 50 –
Ballesteros [8]2014 33 ––
Shahadi [48] 2014 48 35 –
Bazyar [10]2015 35–55 62 –
El-Khamy [15]2016 1 29.2 –
El-Khamy [16] 2017 25 44.6 –
HASFC 100 70.4 37.4
Sheikhan [30]
2010
Kekre [28] 2010
Shahadi [31]
2011
Shahadi [32]
2011
Sheikhan [33]
2011
Shivdas [34]
2014
Ballesteros [9]
2014
Shahadi[35]
2014
Bazyar [29] 2015
El-Khamy [4]
2016
El-Khamy [36]
2017
HASFC
0
10
20
30
40
50
60
70
80
0 20406080100120
SNR (dB)
Hiding Capacity (%)
Fig. 9 Comparison between HASFC and related schemes
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6Summary
This section summarizes the research by focusing on the significant findings and results
highlighted throughout this paper. Several related schemes have adopted temporal domain
while others have used transform domain in order to improve the hiding capacity and preserve
the transparency of the stego audio. The following facts have so far been established:
&The previous scheme has shown to achieve hiding capacity of up to 70% of the audio
cover audio size.
&The highest reported stego fidelity in the previous schemes is at 76 dB.
&The fidelity of the reconstructed stego audio has never been reported before.
&More than 50% of the audio cover audio size is exploited to produce up to 70% hiding
capacity.
&All related schemes did not evaluate with the statistical steganalysis except [8,47].
The proposed model combines temporal and compressed domains by using chaotic LSB
and fractal coding techniques. Nevertheless, the comparison between the HASFC model and
other schemes cuts across the boundary by including schemes from both domains in order to
show the overall potential of the schemes. Based on the results from the experiments and
comparing the results between the HASFC model and the other schemes, the following aspects
have therefore been proven and supported:
&The HASFC model provides 100% hiding capacity, which is 30% higher than that
obtained by the previous method.
&Although the fidelity of the stego audio is marginally lower at 70.4 dB from the previous
highest value, it still well above the acceptable level. Moreover, PRD value is 0.0002 and
SDG is 4.7, on average.
&The proposed model produces SNR of 37.4 dB for the reconstructed audio fidelity value, which
is above the acceptable level. Such value has never been previously reported in the literature.
&The obtained hiding capacity in comparison with the related studies is achieved by altering
only 6.25% of the audio cover audio size as it only uses 1 of 16 bits per cover sample.
Accordingly, the fidelity of the stego-audio is preserved.
&The security of the HASFC model is enhanced using logistic map with their initial
parameter as secret keys.
&HSAFC model is evaluated using fourth first-moment statistical steganalysis and histo-
gram distribution and the results show that the stego signal generated by the HASFC
model can resist this type of steganalysis.
&In general, compression techniques such as fractal coding and existing encryption tech-
niques such as DES and AES produce unreadable files during the encoding phase. Thus,
the possibility for fractal coding to be used in encryption process should be further
investigated.
7 Limitation
Two areas will be addressed in the future for this study. First, the encoding time of fractal
coding can be decreased by accelerating the matching process using different schemes, such as
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multi-threshold and domain block classification. Secondly, the transform domain will be
adopted in the embedding technique to enhance robustness while still maintaining the high
hiding capacity of the proposed model. Furthermore, the resistance of the proposed model
against other steganalysis techniques such as the Reversed Psychoacoustic [18]and
Derivative-Based [34] steganalysis should also be considered.
8 Conclusion
This paper proposes the HASFC model, an audio steganography model that is based on fractal
coding and chaotic LSB. HASFC model utilizes fractal coding in information hiding that
enhances hiding capacity and maintains the transparency of the cover audio. The experimental
results show that fractal coding can be effectively applied to audio steganography similar to
image steganography. On top of that, the HASFC model conclusively produces increasing in
hiding capacity of 30% in comparison with related studies and maintains an acceptable stego
audio fidelity value with SNR of 70.4 dB. At the same time, the fidelity of the reconstructed
secret audio has also proven to be within the satisfactory level with SNR value of 37.4 dB.
Moreover, the results show the resistance of the HASFC model against brute-force attack and
statistical analysis.
Acknowledgements This research is supported by the Ministry of Higher Education and Scientific Research, Studies
Planning and Follow-up Directorate, Republic of Iraq and the Research Center for Software Technology & Management,
Faculty of Information Science and Technology, Universiti Kebangsaan Malaysia (DPP-2015-018).
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Multimed Tools Appl
Ahmed Hussain Ali is a Ph.D. student under the supervision of Dr. Mohd Rosmadi Mokhtar at Universiti
Kebangsaan Malaysia (UKM) - Malaysia, Faculty of Information Science & Technology and Dr. Loay E. George
at University of Baghdad, College of Science, Department of computer Science Iraq. He received M.Sc. degree in
Computer Science, in January 2011 from the College of Science, University of Baghdad –Iraq. His current
research focuses on information security and signal processing.
Loay Edwar George is currently working as a teaching staff member at remote sensing department, college of
science, University of Baghdad. He received his M.Sc. in Theoretical Physics, College of Science, University of
Baghdad, Iraq 1983. He completed his Ph.D. in Digital Image Processing, College of Science, University of
Baghdad, Iraq 1997. His research interests in digital video, image and audio compression techniques, information
hiding in multimedia, biometrics for computer security applications, computer vision, image retrieval systems
and GIS and GPS applications.
Multimed Tools Appl
A. A. Zaidan received the first class B.Eng. degree in Computer Engineering in 2004 from University of
Technology, Baghdad, Iraq. He then continued and received his M.Sc. degree in computer system and network in
2009 from UM, Malaysia. In 2013, he managed to obtain the Ph.D. degree in Computer Engineering from
MMU, Malaysia. Currently, he is working as a senior lecturer at Department of computing, UPSI, Malaysia. His
research areas are Artificial Intelligent,Decision theory,Information security,Multi-Criteria Evaluation and
benchmarking
Mohd Rosmadi Mokhtar is the Deputy Director (Core Applications) in the Center for Information Technology,
Universiti Kebangsaan Malaysia (UKM). He received his Ph.D. in Informatics from The University of Man-
chester in 2011 and Masters in Information Security from Royal Holloway University of London in 2003. His
research interests involve secure digital signal, malware analysis, trust and reputation.
Multimed Tools Appl
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